Screaming Toes: More than an
ice breaker, it's
probability in practice!
How to play:
Get your group together in a big
circle, then everyone looks at someone else's toes, and then everyone looks up, if the person you're looking at is looking at you, you both have to
scream. Naturally, two person screaming toes has the highest probability of a scream, whereas one person screaming toes has the lowest
probability. One person screaming toes with a
mirror might be interesting, though I will not
speculate further.
Now to the more interesting issue, given a set of N people who
randomly look at other people's toes (no person's toes are more attractive than another's), on
average, how many screams should occur per
turn? Here is my solution, though it's probably wrong:
The
event space, E = nCr(N,2)
The
sample space, S = N!
Thus, the probability is
nCr(N,2)/
N! that a given
pair will scream and, on average,
nCr(N,2)/
N! * N people will scream per game.
As it turns out, both 2 and 3 person games have the same probability, .5, (which, remember, is the probability two people will scream) and thus more screams will happen in the 3 person
game.
Don't ask me how this is a
game.